The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty

This study considers a basic inventory management problem with nonzero fixed order costs under interval demand uncertainty. The existing robust formulations obtained by applying well-known robust optimization methodologies become computationally intractable for large problem instances due to the presence of binary variables. This study resolves this intractability issue by proposing a new robust formulation that is shown to be solvable in polynomial time when the initial inventory is zero or negative. Because of the computational efficiency of the new robust formulation, it is implemented on a folding-horizon basis, leading to a new heuristic for the problem. The computational results reveal that the new heuristic is not only superior to the other formulations regarding the computing time needed, but also outperforms the existing robust formulations in terms of the actual cost savings on the larger instances. They also show that the actual cost savings yielded by the new heuristic are close to a lower bound on the optimal expected cost.